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王一 · 2020年03月20日

问一道题：NO.PZ2020021204000037 [ FRM I ]

  1. FRM I
  2. Financial Markets And Products

问题如下：

The Eurodollar futures price for a contract that matures in three years is 95.75. The standard deviation of the change in the short rate in one year is 0.8%. Estimate the continuously compounded forward rate between three and 3.25 years.

解释：

The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on an actual/actual basis.

This rate is compounded quarterly. The rate with continuous compounding is 4 X ln(1 + 0.043090/4) = 0.042860

or 4.2860%. The convexity adjustment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312

An estimate of the continuously compounded forward rate is therefore:

0.042860 - 0.000312 = 0.042548 or 4.255%.

是因为fra的day count 是actual/actual？所以才这样转化的？根据是什么？
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王一 · 2020年03月20日

但是fra本身不就是基于libor的为啥还要再转换day count呢？

1 个答案

袁园_品职助教 · 2020年03月20日

同学你好！

因为libor记利息是按单利（每年360天）算的，但是一年实际是365天，所以单利计息会多出来5天的利息，这里计算比较严谨。

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NO.PZ2020021204000037问题如下The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years.The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. 4.25*365/360=4.3090％4.3090%/4=1.0773％e^1.0773％*4 是这样么？

2024-03-31 21:22 1 · 回答

NO.PZ2020021204000037问题如下 The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years.The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. ​两步计算没看懂

2024-03-31 14:58 1 · 回答

NO.PZ2020021204000037 问题如下 The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years. The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. 最后的一句的问题是说计算连续复利的forwarrate，对吗？Efutures 报价100-R，R是单利，对吗？为什么要计算futures rate连续复利，Efutures 都是连续复利的吗？还是forwarrate 没法计算连续复利？我说清楚了吗，请老师帮解答，谢谢。

2024-03-22 21:24 1 · 回答

NO.PZ2020021204000037 问题如下 The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years. The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. Efutures 报价100-R， R应该是年化的，为什么还要365/360算年化呢？产品适用什么y count convension ,报价中的R就应是这种年化的利率吗？

2024-03-22 15:21 1 · 回答

NO.PZ2020021204000037 问题如下 The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years. The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. 关于y count convention讲义上介绍了三种，actual/actual——T-bonactual/360——money market instruments、30/360——municipbon。在做题过程中，没有那么直接告诉是T-b、money market instruments、municipbon，都是各种金融产品，分不清该用题中的产品适用哪个类型的时间计算，老师有什么好办法吗，怎么运用呢？谢谢老师

2024-03-22 15:03 1 · 回答